Question

A graphing calculator is recommended.Solve the given equation or inequality graphically. State your answers rounded to two decimals.(a) 5x2 − x3 = −x2 + 3x + 4 (Enter your answers as a comma-separated list.)x = (b) 5x2 − x3 ≤ −x2 + 3x + 4 (Enter your answer using interval notation.)x =

Answer 1

a) Given the equation

`5x^2-x^3=-x^2+3x+4`

First, simplify the equation

Then we graph the equation

The solutions are the values of x for which y = 0. These are:

`\begin{gathered} x=-0.58 \\ x=1.29 \\ x=5.29 \end{gathered}`

Answer a: x = -0.58, 1.29, 5.29

b) Given the inequality

`5x^2-x^3\leq-x^2+3x+4`

Solve for x using the graph

So, the solution is:

`\begin{gathered} -0.58\leq x\leq1.29 \\ or \\ x\ge5.29 \end{gathered}`

In interval notation:

`\lbrack-0.58,1.29\rbrack\cup\lbrack5.29,\infty)`

Answer b:

`\lbrack-0.58,1.29\rbrack\cup\lbrack5.29,\infty)`